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A general model-based extended state observer (GMB-ESO) is proposed forsingle-input single-output linear time-invariant systems with a given statespace model, where the total disturbance, a lump sum of model uncertainties andexternal disturbances, is defined as an extended state in the same manner as inthe original formulation of ESO. The conditions for the existence of such anobserver, however, are shown for the first time as 1) the original plant isobservable; and 2) there is no invariant zero between the plant output and thetotal disturbance. Then, the finite-step convergence and error characteristicsof GMB-ESO are shown by exploiting its inherent connection to the well-knownunknown input observer (UIO). Furthermore, it is shown that, with the relativedegree of the plant greater than one and the observer eigenvalues all placed atthe origin, GMB-ESO produces the identical disturbance estimation as that ofUIO. Finally, an improved GMB-ESO with built-in zero dynamics is proposed forthose plants with zero dynamics, which is a problem that has not been addressedin all existing ESO designs.

A General Model-Based Extended State Observer with Built-In Zero Dynamics